There are a number of factors that contribute to the health effect of radioactive materials. Half-life is one. Cobalt-60 has a half-life of 5.25 years. That means, essentially, it's radioactivity does "last a lifetime" if it is kept in the body that long.
Another factor is hold-up in the body, or the converse of hold-up, "clearance". Different chemicals, different compounds are cleared from the body at different rates. Those rates can be *greatly* effected by factors such as diet, general health, age, pregnancy, or by method with which they entered the body, and some others.
The faster a body can clear a poison, the better.
It hapens that metallic and ash-type dusts if injected into the lungs by respiration can have very low clearance. Check out "micro-fine" partiulates and alveoli in your research.
So as I said, a micro-fine particle of cobalt-60 in the lung's alveoli is essentially a death sentence, unless it is removed by surgery or a surgical-type delicate procedure called lavage. It is extremely likely to provoke a lung cancer. Cobalt-60 is a heavy gamma emitter.